... 1998ABSTRACTAn elementary construction using binary codes gives new record kissing numbers in dimensionsfrom 32 to 128.1. IntroductionLet τndenote the maximal kissing number in dimension n, that is, ... 1,260,230,400 in dimensions 32, 64 and 128, for example). In contrast, Quebbemann’s lattice Q32[14], [5, Chap. 8] has τ = 261,120. In recent years the kissing numbers of a few other lattices in dimensions ... survive for long, since our lower bounds forA(n, d)andA(n, d, w) are very weak. However, it is interesting that such a simple constructiongives such dramatic improvements over the kissing numbers...